Question

Derive the equation of the parabola with a focus at (-5, 5) and a directrix of y = -1. (2 points) Please help

Answer 1

Answer: f(x)=1/12(x+5)^2+2

Answer 2

we see that the the parabola opens up since directix is below the focus

for an parabolla opening up/down with vetex at (h,k) and the distance from teh vertex to the focus is p

`(x-h)^2=4p(y-k)`
the distance from vertex to directex is the same as from focus to directix

from (-5,5) and y=-1
that is a vertical distance of 6
vertex is in the middle
6/2=3
5-3=2
the vertex is at (-5,2)
the distance is 3

`(x-(-5))^2=4(3)(y-(2))`

`(x+5)^2=12(y-2)`

`y=(1)/(12)(x+5)^2+2`